Risk of Ruin
The probability that an account's equity reaches a barrier from which it cannot continue — margin exhaustion, a drawdown limit, or zero — before the strategy's edge has time to assert itself.
Risk of ruin is the oldest result in gambling mathematics pointed at a trading account. The classical gambler’s-ruin setup asks: given an edge per bet, a stake size, and a finite bankroll, what is the probability of hitting zero before running indefinitely? The answers carry three lessons that survive every refinement. With a negative edge, ruin is certain given enough play. With a positive edge, ruin is still strictly positive — an edge is not immunity, only a tendency. And the probability is savagely nonlinear in stake size: betting twice as large does not double the risk of ruin, it can raise it by orders of magnitude, because ruin is driven by the tail of loss sequences and the tail compounds.
Textbook treatments then observe that fixed-fractional sizing drives classical ruin toward zero — a fraction of a shrinking bankroll can never quite reach nothing. Real accounts are not so lucky, because real ruin barriers sit far above zero: the margin call, the prop firm’s daily loss limit, the trailing drawdown floor, the investor’s redemption trigger, the trader’s own capitulation. Ruin is properly defined by the nearest binding barrier, and against those barriers fractional sizing offers no asymptotic escape. Fat-tailed returns and correlated positions — five trades that are secretly one trade — raise the probability further beyond what Gaussian intuition suggests.
The statistic’s honest use is conditional. Given a sizing rule, a barrier, and an estimated edge, risk of ruin is computable, and the computation is genuinely decision-relevant: it converts “how much should I risk?” into an explicit survival probability. But it is conditioned on the edge estimate, and edge estimates inherited from an overfit backtest are inflated — which means the computed ruin probability is understated at exactly the moment it is being relied upon. A ruin calculation is only as honest as the drawdown and return distributions fed into it.